Gordon Brown remains prime minister, and government business continues, with Chancellor Alistair Darling attending a meeting of finance ministers in Brussels.
Mr Brown has offered the Lib Dems talks if no deal is reached with the Conservatives.
While the negotiations took place, Mr Brown met Mr Clegg at the Foreign Office, having arrived back at Downing Street on Sunday afternoon from his home in Scotland.
A Downing Street spokesman said in a text message to the BBC: "Gordon Brown phoned Nick Clegg last night. Following the discussion they met at the Foreign Office to update each other.
"This was an amicable discussion."
Mr Cameron was aware of the meeting.
BBC political editor Nick Robinson said of the Tory-Lib Dem negotiations: "They are not merely going through the motions. There are real and substantial talks."
He added: "It is make your mind up time for Nick Clegg and the Lib Dems.
"They don't have to do it now, they don't have to do it tomorrow [Monday] - but they do have to do it pretty soon."
The Conservative negotiating team consisted of William Hague, shadow chancellor George Osborne, policy chief Oliver Letwin and chief of staff Ed Llewellyn.
Their Lib Dem counterparts were MPs Chris Huhne - Lib Dem home affairs spokesman - Andrew Stunell, David Laws and chief of staff Danny Alexander.
Mr Hague, emerging from the Cabinet Office after a day of talks, said: "The issues that we have covered have included political reform, economic issues and reduction of the deficit, banking reform, civil liberties, environmental issues.
"So, we've had good discussions about all of those areas.
"We are agreed that a central part of any agreement that we make will be economic stability and the reduction of the budget deficit, but each negotiating team is now going to report to our party leaders."
Minutes later, Mr Alexander also made a brief statement, describing the talks as wide-ranging and "good", and also emphasised that deficit reduction was important.
Shadow Foreign Secretary William Hague: 'We will meet Lib Dems again'
Earlier, Michael Gove, who said he would give up a cabinet seat for a Lib Dem, said the Lib Dems would not be "manoeuvred" into accepting an unsatisfactory deal.
Mr Gove, on the BBC's Andrew Marr programme, said he would like to see a "spirit of co-operation" between the Conservatives and Lib Dems.
"We must be respectful of what the Liberal Democrats want to do. We're not attempting to sandbag or manoeuvre them into a situation with which they are unhappy."
He said he was prepared to give up his potential position as education secretary for a Liberal Democrat. Currently David Laws is the Lib Dems education spokesman.
Mr Clegg, speaking on Sunday before talks resumed, said: "I'm very keen the Liberal Democrats should play a constructive role at a time of great economic uncertainty to provide a good government that this country deserves.
"Throughout that we will continue to be guided by the big changes we want."
'Listening to Labour'
Nick Clegg: "Everyone's trying to be constructive"
The Lib Dem leader has said the Conservatives, as the biggest party, have the right to seek to form a government first.
They have met the Tory team three times, assisted by civil servants as agreed in the arrangements for a hung parliament.
Mr Cameron and Mr Clegg first met for face-to-face talks over a possible coalition on Saturday and discussed it again by phone a day later.
Former Lib Dem leader Lord Ashdown said it was important that the party talks to the Conservatives at the same time as "listening to Labour".
"The central proposition is: what combination serves the nation's interests in providing stable, long-term stability in order to tackle the crisis?" he said.
During the day, Mr Brown met Business Secretary Peter Mandelson, advisor Alastair Campbell, energy secretary Ed Miliband and deputy leader Harriet Harman earlier in Downing Street.
In an e-mail, the prime minister thanked Labour activists for their work throughout the election.
If they wish to talk to us, we're ready to talk to them
"The past few days have seen us enter a political landscape not considered possible a few short weeks ago - with the outcome of the election leading to no single party able to form a majority government," he wrote.
"My duty as prime minister has been to seek to resolve this situation."
Several Labour backbenchers have called for Mr Brown to step down.
MP George Howarth, a minister in the Blair government, said the only people capable of forming any kind of government were the Conservative Party, and that Labour should become a "constructive" opposition.
But Labour party treasurer Jack Dromey said the "big choice" was for Mr Clegg about whether to be a progressive party or "get into bed with the heirs of Mrs Thatcher".
"If they wish to talk to us, we're ready to talk to them," Mr Dromey said, a sentiment echoed by Mr Darling.
Scotland's First Minister, SNP leader Alex Salmond, called on the Lib Dems to join a "progressive alliance" involving Labour, the SNP and Plaid Cymru.
The Tories secured 306 of the 649 constituencies contested on 6 May. It leaves the party short of the 326 MPs needed for an outright majority, with the Thirsk and Malton seat - where the election was postponed after the death of a candidate - still to vote.
Labour finished with 258 MPs, down 91, the Lib Dems 57, down five, and other parties 28.
If Labour and the Lib Dems joined forces, they would still not be the largest grouping. With the support of the Northern Irish SDLP, one Alliance MP, and nationalists from Scotland and Wales they would reach 328, rising to 338 if the DUP, the independent unionist and the new Green MP joined them.
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